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The IDdAM special period in Padova consists of two intensive months devoted to the study of the Langlands Program.  The Langlands program is a centerpiece of research in modern number theory incorporating and animating research in such diverse fields as representation theory, complex analysis, arithmetic geometry, and algebraic topology. Its ultimate goal is to relate analytic objects (automorphic forms) with objects of algebraic nature (Galois representations). Progress in this area have been extremely fast in the past 20 years and have received the highest interest by the international scientic community, see for instance the talks at the ICM given by L. Laorgues (2002), N. Chau, C. Breuil (2010), M. Emerton, J. Arthur, M. Harris (2014).